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Problem 21

In Exercises 21-40, find the quotient \(\frac{z_{1}}{z_{2}}\) and express it in rectangular form. $$ z_{1}=6\left(\cos 100^{\circ}+i \sin 100^{\circ}\right) \text { and } z_{2}=2\left(\cos 40^{\circ}+i \sin 40^{\circ}\right) $$

Problem 21

In Exercises 13-40, perform the indicated operation, simplify, and express in standard form. $$ 3(4-2 i) $$

Problem 21

In Exercises 21-36, each set of parametric equations defines a plane curve. Find an equation in rectangular form that also corresponds to the plane curve. $$ x=\frac{1}{t}, y=t^{2} $$

Problem 21

In Exercises 13-28, express each complex number in polar form. $$ 3+0 i $$

Problem 21

In Exercises 21-40, convert each point given in polar coordinates to exact rectangular coordinates. $$ \left(4, \frac{5 \pi}{3}\right) $$

Problem 22

In Exercises 13-28, express each complex number in polar form. $$ -2+0 i $$

Problem 22

In Exercises 21-40, find the quotient \(\frac{z_{1}}{z_{2}}\) and express it in rectangular form. $$ z_{1}=8\left(\cos 80^{\circ}+i \sin 80^{\circ}\right) \text { and } z_{2}=2\left(\cos 35^{\circ}+i \sin 35^{\circ}\right) $$

Problem 22

In Exercises 13-40, perform the indicated operation, simplify, and express in standard form. $$ 4(7-6 i) $$

Problem 22

In Exercises 21-36, each set of parametric equations defines a plane curve. Find an equation in rectangular form that also corresponds to the plane curve. $$ x=t^{2}-1, y=t^{2}+1 $$

Problem 22

In Exercises 21-40, convert each point given in polar coordinates to exact rectangular coordinates. $$ \left(2, \frac{3 \pi}{4}\right) $$

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